Dynamical analysis of a forced vibrating planar motion of a spring pendulum

Abstract

This work studies the nonlinear movement of a two degrees-of-freedom (DOF) spring pendulum that is dampened and affected by a torque and harmonic force externally. It is presumed that the spring’s pivot point travels along an elliptic route. Lagrange's equations are utilized to generate the regulating system of motion. The multiple-scales approach (MSA) is used to gain the system’s analytic solutions up to the third approximation. Therefore, all resonance cases that have emerged are categorized, wherein two of them are scrutinized at once. As a result of the removal of secular terms, the solvability constraints are attained and then the steady-state solutions are investigated. The examined motion's temporal evolution, the resonance response curves, and the solutions at the steady-state are all depicted graphically. In compliance with the Routh-Hurwitz criteria (RHC), all possible fixed points (FP) for the cases of steady and unsteady are found and displayed. The stability zones are examined and analysed to estimate the effect of various factors on the system’s behavior. This model has gained prominence recently due to its industrial uses in fields including construction, infrastructure, transportation, and vehicles.